Mathematical Sciences: Qualitative Behavior of Solutions to Nonlinear Problems in Elasticity

主要研究者将研究定性 一类问题的解的行为， 多维弹性 需要考虑的问题是 平衡问题的现实模型的同质， 二维和三维的各向同性超弹性材料。 特别地，储存的能量在这些问题中起作用 爆破作为变形梯度的决定因素 接近于零。 该项目的主要目标是确定先验 解的正则性和定性行为。 的 主要研究者还将研究 解决方案以及解决方案的定性性质， 具体的边值问题，例如描述 超弹性杆的单轴拉伸

The principal investigator will study the qualitative behavior of solutions to a class of problems from multidimensional elasticity. The problems to be considered are equilibrium problems for realistic models of homogeneous, isotropic, hyperelastic materials in two and three dimensions. In particular, the stored energy functions in these problems blow up as the determinant of the deformation gradient approaches zero. The main goal of the project is to determine a priori regularity and qualitative behavior of solutions. The principal investigator will also investigate uniqueness of solutions as well as qualitative properties of solutions to specific boundary value problems, such as the one describing uniaxial extension of a hyperelastic bar.